Not sure what's happening with the TextBlock - all my experience says that some combination of HorizontalContentAlignment and HorizontalAlignment (on both the StatusBar and the TextBlock) should achieve what you want. Anyway - hopefully the StatusBarItem will work for you.

For anyone who is looking for the answer to the question in the title (not necessarily for use in a status bar), I found a Label to be better than a TextBlock for having control over alignment and still feeling semantically correct.